Hierarchical Techniques

Step 1. Calculation of the between-object distance matrix. 

Step 2. Find the smallest elements in the distance matrix and join the corresponding objects into a single cluster. 

Step 3. Calculate a new distance matrix, taking into account that clusters produced in the second step will have formed new objects and taken the place of original data points. 

Step 4. Return to Step 2 or stop if the final two clusters have been fused into the final, single cluster. 

The wide range of agglomerative methods available differ principally in the implementation of Step 3 and the calculation of the distance between two clusters. The different between-group distance measures can be defined in terms of the general formula 

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Hierarchical Techniques. Classes are subclassified into groups, with the process being repeated at several levels to produce a tree which gives sufficient definition to groups. 

The principal aim of performing a cluster analysis is to permit the identification of similar samples according to their measured properties. Hierarchical techniques, as we have seen, achieve this by linking objects according to some formal rule set. The K-means method on the other hand seeks to partition the pattern space containing the objects into an optimal predefined number of... 

Hierarchical clustering procedures iteratively partition the item set into disjointed subsets. There are top-down and bottom-up techniques. The top-down techniques partition can be into two or more subsets, and the number of subsets can be fixed or variable. The aim is to maximize the similarity of the items within the subset or to maximize the difference of the items between subsets. The bottom-up techniques work the other way around and build a hierarchy by assembling iteratively larger clusters from smaller clusters until the whole item set is contained in a single cluster. A popular hierarchical technique is nearest-neighbor clustering, a technique that works bottom up by iteratively joining two most similar clusters to a new cluster. 

There are basically two approaches to data clustering, dynamic methods and hierarchical techniques. 

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